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Please explain the accelaration due to gravity below and above the surface of the earth in an easy manner with the derivation ?


Consider an object of mass m lying on or near the surface of the Earth. Let M_{e} be the mass of the Earth and R_{e} be its radius i.e., R_{e} is the distance between the object and the centre of the Earth.
According to Newton's law of gravitation, the force of attraction (F) between the Earth and the object is
A Body of Mass m Lying on the Surface of the Earth
According to Newton's second law of motion this force produces an acceleration (g) in the object.
F = ma (a = g)
F = mg
Substituting the value of F in equation (2) we get,
From equation (3) it is very clear that acceleration due to gravity does not depend on the mass m of the object. It only depends on the mass of the Earth (M_{e}) and the distance from the centre of the Earth to the object.
Numerical Value of Acceleration due to Gravity on Earth
Gravitational Constant (G) = 6.6734 x 10^{}^{1}^{1} Nm^{2}/kg^{2}
Mass of the Earth (M_{e}) = 6 x 10^{2}^{4} kg
Radius of the Earth (R_{e}) = 6.4 x 10^{6} m